Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries

To solve the disadvantages of high difficulty and complexity in studying the spatial topological relation method on different resolution remote sensing images, this paper proposes a spatial topological relationship model based on GeoSOT, which is one of the global subdivision grids. To express spatial objects on different resolution remote sensing images, this paper introduces the spatial objects subdivision location identification. Then, the model calculates spatial topological relation by comparing location identifications in combined table. At last, test shows that it is feasible to analyze the spatial objects topological relations based on GeoSOT and it has high efficiency operation significantly, especially for complicated spatial objects.

An abstract examination of refinement (and conversely, coarsening) with respect to the involved spatial relations gives rise to formulated order relations between spatial coverings, which are defined as complete-coverage representations composed of regional granules. Coverings, which generalize partitions by allowing granules to overlap, enhance hierarchical geocomputations in several ways. Refinement between spatial coverings has underlying patterns with respectto inclusion—formalized as binary topological relations— between their granules. The patterns are captured by collection relations of inclusion, which are obtained by constraining relevant topological relations with cardinality prop- erties such as uniqueness and totality. Conjoining relevant collection relations of equality and proper inclusion with the overlappedness (non-overlapped or overlapped) of the re- fining and the refined covering yields collection order relations, which serve as specific types of refinement between spatial coverings. The examination results in 75 collection order relations including seven types of equality and 34 pairs of strict or non-strict types of refinement and coarsening, out of which 19 pairs form partial collection orders.

This paper considers the nineteen planar discrete topological relations that apply to regions bounded by a digital Jordan curve. Rather than modeling the topological relations with purely topological means, metrics are developed that determine the topological relations. Two sets of five such metrics are found to be minimal and sufficient to uniquely identify each of the nineteen topological relations. Key to distinguishing all nineteen relations are regions’ margins (i.e., the neighborhood of their boundaries). Deriving topological relations from metric properties in \( {\mathbb{R}}^{2} \) vs. \( {\mathbb{Z}}^{2} \) reveals that the eight binary topological relations between two simple regions in \( {\mathbb{R}}^{2} \) can be distinguished by a minimal set of six metrics, whereas in \( {\mathbb{Z}}^{2} \), a more fine-grained set of relations (19) can be distinguished by a smaller set of metrics (5). Determining discrete topological relations from metrics enables not only the refinement of the set of known topological relations in the digital plane, but further enables the processing of raster images where the topological relation is not explicitly stored by reverting to mere pixel counts.KeywordsDiscrete spatial regionsSpatial reasoningModel interoperabilityTopological relationsSpatial queriesGeographic information systems

Representing and reasoning about the topological relationships has attracted many discussions in the GIS field, several formalized descriptive model was proposed. As GIS is developing towards 3D (three dimensional), one of the most difficult problems is spatial analysis, especially the topology analysis. This article aims to provide a simple solution to the issue of judging the topological relation between a line and a connected region without holes in 3D space based on the DE-9IM (Dimensionally Extended 9-Intersection Model). We will discuss how to use the DE-9IM to describe the binary topological relations between regions and lines in 3D. A set of possible existing topological relations between a line and a region in three-dimensional space will be given out, and the algorithm of judging the topological relations mentioned above will be explored in detail.

The technological progress in the field of artificial intelligence (AI) has brought new opportunities and challenges to the intelligent development and innovative research in fuzzy spatial relations, fuzzy theory is the basic theory of intelligent information processing, and the paper gives a brief analysis of fuzzy calculation method in spatial analysis and spatial relation calculation. In particular, the spatial relations of fuzzy objects are more difficult to express and describe accurately. This paper proposes a method to calculate the topological relations between fuzzy objects with 4-Intersection model and 9-Intersection model, in the analysis of spatial relations, the extension from deterministic entity to uncertain entity is realized with fuzzy set theory, the fuzzy space matrix is constructed, then fuzzy topological relations and fuzzy membership are calculated and output, the model simplifies many complex relations, and it can describe eight topological relations including disjoint, meet, overlap, covers, contains, covered-by, inside and equal. In practical application, the position of spatial objects can be controlled and adjusted according to topological relations. Through analysis of algorithm and fuzzy membership calculation, the model is effective in theory.

Representing topological information for the Semantic Web often involves qualitative defined natural language terms such as “In”. This can be the case when exact coordinates of spatial regions are not available or they are unreliable. Topological spatial relations are the most important aspect of spatial representation and reasoning. In addition to topology, often the exact size of regions is not known as well, but the relations between sizes (e.g., larger, equal) are known. In this work we propose and evaluate an integrated representation of topological relations (RCC-5 and RCC-8) and qualitative size relations using OWL object properties and axioms, combined with reasoning rules expressed using SWRL, embedded into the ontology. Different representations are implemented and evaluated.KeywordsSpatial Representation and ReasoningSemantic WebRules

Directional relations, topological relations and metric relations are the basic spatial constraint in the geometric space. The three kinds of spatial relations are not isolated and restrict each other. In this paper, we focus on the effect of topology and distance on the representation of directional relations and present a description mechanism of directional relations considering topology and distance. In this new model, (1)topological constraint is analyzed as the basis of directional relations categories; (2)distance relations is the other factor of representation of directional relations and distinguish the directional relations of different positions in the same ray line; (3)depending on the analysis of the capability of exiting directional relations models to represent the restraint from the topological relations and distance, a category mechanism based on the topological relations and distance is proposed to improve the accuracy of the directional description. This model combines the restraint from topological and distance relations and consummates the representation of directional relations. Experiments show excellent efficiency in view of directional description.

For remote sensing imagery, spatial relationships are extracted by segmentation and classification. Unlike traditional vector relationships, spatial relationship reasoning is equivalent to constraint satisfaction problems in the image process. Based on 9-intersect model, the paper discuss spatial topological relationship between image objects to provide a theoretical and technical support for low levels of image segmentation, high-level analysis.

Spatial modeling is one of the most important parts in the area of spatial relations, and it is necessary to develop a new model with high practicality. Firstly this paper analyzes the characteristics and defects of present models; secondly introduces in detail the construction method of quadtree histogram; thirdly cloud model are used to judge spatial directional relation. The experimental results show that the model is feasible. Computer vision is concerned with automatic extraction of useful information from images. The description for human space perception is an important task of the computer vision research. The description of spatial relation is a basic ability of human cognition, it is an important basic task for computer audio-visual information processing to build automatically the description of spatial relation between objects in the image. Spatial relation is mainly constituted of directional relation, topological relation and distance relation. The fundamental theories of topology relation and distance relation are comparatively perfect, but the fundamental theories of directional relation have not any unified standard. There are three main approaches for assessing the basic directional relation. The first one is based on cone model (1) which assimilates an object to the centroid, but it doesn't take into account shape, size and distance information. The second one is based on projection model such as minimum bounding rectangles (2), and directional relation matrix (3), etc., but these models assimilate an object to the minimum bounding rectangle, so shape, size and distance information also can't be taken into account. The third one is based on angle-histogram model (4). Given an object of target A and a reference object B, the angle-histogram is computed from the angles between any two points in both objects and normalized by the maximum frequency. This histogram represents the directional relations of the object A with respect to the reference object B. This model has taken into account shape, size and distance information. But this model has high computational complexity, so it is not practical. Numerous studies are based on this notion of angle-histogram, e.g., (5-8). In (5-7), R-histogram, R*-histogram and F-histogram are proposed, and they can reduce the computational complexity. In (8), a quadtree histogram model of spatial directional relation is proposed, and it can get high accuracy and small computational complexity together.

By researching and analyzing the crop diseases and insect pests, we find the distribution and spread of crop diseases and insect pests have tight touch with the time and space information, which provides a premise of applying geography information system (GIS) and spatial interpolation technology especially. By considering the particularity of spatial interpolation on the plant diseases and insect pests in agriculture, the authors bring forward one new method: multifactors spatial interpolation model. It is made up of many factors, such as spatial orientation relationship, topological relationship, distance relationship and national weather conditions so on. Then, on the basis of building the multi-factors spatial interpolation model, the monitor and warning system of crop diseases and insect pests is constructed by using GIS technology and ArcIMS software. The basic functions, such as map visualization, information query, data input, data management, spatial interpolation, are implemented. What's more, by using the multi-factors spatial interpolation model, the effluence and spread speed of crop diseases and insect pests are showed and the monitoring and early-warning of crop diseases and insect pests is implemented.

For qualitative spatial reasoning, there are various dimensions of objects. A considerable amount of effort has been devoted to 2D representation and analysis of spatial relations. Here we present an exposition for 3D objects. There are three types of binary relations between pairs of objects: topological connectivity, cardinal directions, and distance relations. The combinations of these relations can provide additional useful knowledge. The spatial databases include data and the spatial relations to facilitate end-user spatial querying, it also is important to associate natural language with these relations. Some work has been done in this regard for line-region and region-region topological relations in 2D, and very recent work has initiated the association between natural language, topology, and metrics for 3D objects. However, prior efforts have lacked rigorous analysis, expressive power, and completeness of the associated metrics. Herein we present a detailed study of new metrics required to bridge the gap between topological connectivity and size information for integrating reasoning in spatial databases. The complete set of metrics that we present should be useful for a variety of applications dealing with 3D objects including regions with vague boundaries.

Spatial relation between spatial objects is a very important topic for spatial reasoning, query and analysis in global GIS. However, the most popular models in current use, which are based on the 2D Euclidean space (such as raster), exist some fundamental deficiency in theory for spatial relation reasoning in the spherical digital space (SDS). In this paper, a reasoning method of spatial relations in the SDS based on manifold is approached, in which: (1) the topological definitions, properties, and descriptions of spatial objects in SDS are presented; (2) appropriate operators from set operators (i.e. intersection, difference, difference by, symmetric difference, etc.) are utilized to distinguish the spatial relations between neighboring spatial objects; and (3) the value of the Euler number of symmetric difference is used for the detailed computational results of set operations; In this method, the 8 types basic topological relations between spatial objects in SDS can be distinguished accurately and easily from simple to detailed level for different requirements.

Cloud computing technology is changing the mode of the spatial information industry which is applied and provides new ideas for it. Since Hadoop platform provides easy expansion, high performance, high fault tolerance and other advantages, we propose a novel vector spatial data storage schema based on it to solve the problems on how to use cloud computing technology to directly manage spatial data and present data topological relations. Firstly, vector spatial data storage schema is designed based on column-oriented storage structures and key/value mapping to express spatial topological relations. Secondly, we design middleware and merge with vector spatial data storage schema in order to directly store spatial data and present geospatial data access refinement schemes based on GeoTools toolkit. Thirdly, we verify the middleware and the data storage schema through Hadoop cluster experiments. Comprehensive experiments demonstrate that our proposal is efficient and applicable to directly storing large-scale vector spatial data and timely express spatial topological relations.

The spatial relation model is an important technique for image indexing and retrieval in image or multimedia databases. 2D strings and its variants are proposed to support the representation of spatial relationships. A novel spatial knowledge representation model named “Two Dimension Begin-End boundary string” (2D Bε-string) is proposed. The 2D Bε-string represents an icon by its MBR boundaries. By applying a number of “dummy objects”, the 2D Bε-string can intuitively and naturally represent the pictorial spatial information without any spatial operator. In addition, an image similarity evaluation method based on the modified “Longest Common Subsequence” (LCS) algorithm is presented. By using the proposed evaluation method, not only can those images for which all the icons and their spatial relationships fully agree with the query image be sifted out, but also those images whose partial icons and/or spatial relationships are similar to the query image. It resolves the problems of query targets and/or spatial relationships not being certain. Our representation model and similarity evaluation also simplify the retrieval progress of linear transformations, including image rotation and reflection

Landform recognition is one of the most significant aspects of geomorphology research, which is the essential tool for landform classification and understanding geomorphological processes. Watershed object-based landform recognition is a new spot in the field of landform recognition. However, in the relevant studies, the quantitative description of the watershed generally focused on the overall terrain features of the watershed, which ignored the spatial structure and topological relationship, and internal mechanism of the watershed. For the first time, we proposed an effective landform recognition method from the perspective of the watershed spatial structure, which is separated from the previous studies that invariably used terrain indices or texture derivatives. The slope spectrum method was used herein to solve the uncertainty issue of the determination on the watershed area. Complex network and P–N terrain, which are two effective methodologies to describe the spatial structure and topological relationship of the watershed, were adopted to simulate the spatial structure of the watershed. Then, 13 quantitative indices were, respectively, derived from two kinds of watershed spatial structures. With an advanced machine learning algorithm (LightGBM), experiment results showed that the proposed method showed good comprehensive performances. The overall accuracy achieved 91.67% and the Kappa coefficient achieved 0.90. By comparing with the landform recognition using terrain indices or texture derivatives, it showed better performance and robustness. It was noted that, in terms of loess ridge and loess hill, the proposed method can achieve higher accuracy, which may indicate that the proposed method is more effective than the previous methods in alleviating the confusion of the landforms whose morphologies are complex and similar. In addition, the LightGBM is more suitable for the proposed method, since the comprehensive manifestation of their combination is better than other machine learning methods by contrast. Overall, the proposed method is out of the previous landform recognition method and provided new insights for the field of landform recognition; experiments show the new method is an effective and valuable landform recognition method with great potential as well as being more suitable for watershed object-based landform recognition.